Arabzadeh et al. (2026) A surrogate-aided approach for accelerated Bayesian calibration of hydrologic models

Identification

• Journal: Environmental Modelling & Software
• Year: 2026
• Date: 2026-01-24
• Authors: Rezgar Arabzadeh, Jonathan Romero-Cuellar, James Craig, Bryan A. Tolson, Robert Chlumsky
• DOI: 10.1016/j.envsoft.2026.106894

Research Groups

• University of Waterloo, Department of Civil and Environmental Engineering, Canada

Short Summary

This study introduces a surrogate-aided error model (SHA) using Support Vector Regression (SVR) to decouple the inference of hydrologic and error model parameters in Bayesian calibration. The approach significantly accelerates convergence, requiring approximately 50% fewer samples, and consistently improves or maintains predictive accuracy across 12 MOPEX watersheds using the GR4J model.

Objective

• To develop and demonstrate a surrogate-aided approach for Bayesian calibration of hydrologic models that decouples the inference of hydrologic and error model parameters, thereby accelerating convergence and improving predictive accuracy.

Study Configuration

• Spatial Scale: 12 MOPEX watersheds across the continental United States (specifically the southeastern portion), ranging from 1023 km² to 4419 km² in area. Each watershed was modeled as a single Hydrologic Response Unit (HRU) using a lumped model approach.
• Temporal Scale: 56 years of daily hydrometeorological and streamflow data (1948–2003) for calibration and evaluation.

Methodology and Data

• Models used:
  • Hydrologic model: GR4J (with CEMANeige snow model and lapse-rate adjustments) implemented in the Raven framework.
  • Surrogate model: Support Vector Regression (SVR) for estimating error model parameters.
  • Inference algorithm: No-U-Turn Sampler (NUTS) from the LaplacesDemon R package for Bayesian inference.
  • Error models benchmarked: Surrogate-aided Heteroscedastic Autocorrelated error model (SHA), Heteroscedastic Autocorrelated error model with Student's t-distribution (THA), Homoscedastic, uncorrelated error model with Gaussian distribution (G), Gaussian Heteroscedastic Autocorrelated model (GHA).
• Data sources:
  • MOPEX12 watersheds hydrometeorological and streamflow data, publicly available from NOAA (ftp://hydrology.nws.noaa.gov/pub/gcip/mopex/USData/).
  • Data and model setups archived at https://github.com/rarabzad/GR4JMOPEX/tree/main.

Main Results

• The surrogate-aided approach (SHA) achieved significantly faster convergence in Bayesian calibration, reaching the Gelman-Rubin (GR) convergence threshold of 1.1 at approximately 40,000 samples for the Guadalupe watershed, while other methods (THA, GHA) persisted above this threshold.
• SHA required approximately 49.2% fewer MCMC samples to converge compared to THA (38,350 ± 3795 samples vs. 75,430 ± 7230 samples) and 52.1% fewer than GHA (38,350 ± 3795 samples vs. 80,130 ± 6358 samples).
• This reduction in sample size translated to substantial computational time savings, with SHA completing calibration in 6.5 ± 0.6 hours, which is 48.4% faster than THA (12.6 ± 1.2 hours) and 51.5% faster than GHA (13.4 ± 1.1 hours).
• SHA consistently demonstrated superior predictive accuracy, exhibiting the lowest median Continuous Ranked Probability Score (CRPS) and a narrower interquartile range across all 12 MOPEX watersheds.
• The method achieved a favorable balance between predictive reliability (coverage of observed flows) and sharpness (narrowness of credible intervals).
• The SVR model effectively mapped hydrologic parameters to error model parameters, achieving a mean R² of 0.89 ± 0.06 for error model parameter prediction across all MOPEX12 watersheds with 1000 training samples.

Contributions

• Introduces a novel surrogate-aided error model (SHA) that decouples the inference of hydrologic and error model parameters in Bayesian calibration, addressing the challenge of slow convergence due to high-dimensional interactions.
• Demonstrates the effective use of Support Vector Regression (SVR) as a surrogate to deterministically estimate error model parameters conditional on hydrologic parameters within an MCMC sampler.
• Achieves significant computational efficiency gains, reducing both the required number of MCMC samples (approximately 50%) and calibration runtime (approximately 50%) compared to traditional joint inference methods.
• Consistently improves or maintains predictive accuracy, as evidenced by lower CRPS values and a better balance of reliability and sharpness in probabilistic streamflow predictions.
• Provides a promising framework for efficient operational hydrologic applications, large-scale modeling, and real-time streamflow forecasting, particularly when computational resources are limited.

Funding

• NSERC Discovery grants: RGPIN-2017-03920, RGPIN-2023-03459 (J. Craig); RGPIN-2022-03890 (B. Tolson)
• NSERC Tier II Canada Research Chair in Hydrologic Modeling and Analysis: CRC-2020-00176 (J. Craig)
• NSERC Collaborative Research and Development Grant: 536471-18 (supported by Ontario Power Generation)

Citation

@article{Arabzadeh2026surrogateaided,
  author = {Arabzadeh, Rezgar and Romero-Cuellar, Jonathan and Craig, James and Tolson, Bryan A. and Chlumsky, Robert},
  title = {A surrogate-aided approach for accelerated Bayesian calibration of hydrologic models},
  journal = {Environmental Modelling & Software},
  year = {2026},
  doi = {10.1016/j.envsoft.2026.106894},
  url = {https://doi.org/10.1016/j.envsoft.2026.106894}
}